Chapter 3 -- vocabulary
preferential trade agreement -- a mechanism that confers special treatment on select trading partners
free trade area (FTA) -- formed when two or more countries agree to eliminate tariffs and other barriers that restrict trade
free trade agreement -- the ultimate goal of which is the rare duties on goods that cross borders between the partners
rules of origin -- used to discourage the importation of goods into the member country
customs union -- represents the logical evolution of a free trade area
common external tariffs (CETs) -- When a goup of countries form a customs union they must introduce a common external tariff. The same customs duties, quotas, preferences or other non-tariff barriers to trade apply to all goods entering the area, regardless of which country within the area they are entering. It is designed to end re-exportation
common market -- Where two or more countries agree to form a customs union between themselves and a common external tariff against goods and commodities imported from other countries
economic union -- builds upon the elimination of the internal tariff barriers, the establishment of common external barriers, and the free flow of factors. It seeks to coordinate harmonize economic and social policy within the union to facilitate the free flow of capital, labor, and goods and services from country to country
Saturday, June 23, 2007
in the global trade environment
Chapter 3 -- summary
The multilateral World Trade Organization, created in 1995 as the successor to the General Agreement on Tariffs and Trade, provides a forum for settling disputes among member nations and tries to set policy for world trade. The world trading environment is also characterized by preferential trade agreements among smaller numbers of countries on the regional and some regional basis. These agreements can be conceptualized on a continuum of increasing economic integration. Free trade areas such as the one created by the North American Free Trade Agreement (NAFTA) represent the lowest level of economic integration. The purpose of a free trade area is to eliminate tariffs and quotas.
Rules of origin are used to verify the country from which the goods are shipped. A customs union represents a further degree of integration in the form of common external tariffs. And a common market such as the Central American Integration System (SICA), restrictions on the movement of labor and capital are based in an effort to further increase integration. In an economic union, such as the European Union (EU), the highest level of economic integration is achieved by unification of economic policies and institutions. Other important call Thracian agreements include the Association of Southeast Asian Nations (ASEAN) and Quad ration Council for the Arab States of the Golf (GCC). In Africa, the two main cooperation agreements are the Economic Community of West African States (ECOWAS) and the South African Development and community (SADC).
The multilateral World Trade Organization, created in 1995 as the successor to the General Agreement on Tariffs and Trade, provides a forum for settling disputes among member nations and tries to set policy for world trade. The world trading environment is also characterized by preferential trade agreements among smaller numbers of countries on the regional and some regional basis. These agreements can be conceptualized on a continuum of increasing economic integration. Free trade areas such as the one created by the North American Free Trade Agreement (NAFTA) represent the lowest level of economic integration. The purpose of a free trade area is to eliminate tariffs and quotas.
Rules of origin are used to verify the country from which the goods are shipped. A customs union represents a further degree of integration in the form of common external tariffs. And a common market such as the Central American Integration System (SICA), restrictions on the movement of labor and capital are based in an effort to further increase integration. In an economic union, such as the European Union (EU), the highest level of economic integration is achieved by unification of economic policies and institutions. Other important call Thracian agreements include the Association of Southeast Asian Nations (ASEAN) and Quad ration Council for the Arab States of the Golf (GCC). In Africa, the two main cooperation agreements are the Economic Community of West African States (ECOWAS) and the South African Development and community (SADC).
Friday, June 22, 2007
the global economic environment
Chapter 2 -- vocabulary
market capitalism -- an economic system in which individuals and firms allocate resources and production resources are privately owned. Consumers decide what goods they desire and firms determined what and how much to produce
Centrally planned socialism -- the state has broad powers to serve the public interest as it sees fit. State planners may decisions about what goods and services are produced and in what quantities; consumers spend their money on what is available. Government ownership of entire industries, as well as individual enterprises
centrally planned capitalism and economic system in which command resource allocation is utilized extensively in an environment of private resource ownership
market socialism -- Mark allocation policies are permitted within an overall environment of state ownership
G-7 -- Group of 7 -- high income countries, the United States, Japan, Germany, France, Britain, Canada, and Italy. Finance ministers, central bankers, and heads of state from the seven nations have worked together for a quarter of a century in an effort to steer the global economy in the direction of prosperity and to ensure monetary stability
Organization for Economic Cooperation and Development (OECD) -- institution comprised of high income countries, the 30 nations that belong to the OECD believe in market allocation economic systems and pluralistic democracy
The Triad -- Japan, Western Europe, and the United States. These three regions, represent the dominant economic centers of the world. Today, nearly 75% of the world income is located in the Triad
purchasing power parity (PPP) --Model of exchange rate determination stating that the price of a good in one country should equal the price of the same good in another country, exchanged at the current rate
economic exposure -- impact of currency fluctuations on the present by you of the companies expected future cash flows
transaction exposure -- arises when the companies activities result in sales or purchases denominated in foreign currencies
hedging --Reducing exposure to risk of loss resulting from fluctuations in exchange rates, commodity prices, interest rates etc
forward market -- a mechanism for buying and selling currencies and a preset price for future delivery
market capitalism -- an economic system in which individuals and firms allocate resources and production resources are privately owned. Consumers decide what goods they desire and firms determined what and how much to produce
Centrally planned socialism -- the state has broad powers to serve the public interest as it sees fit. State planners may decisions about what goods and services are produced and in what quantities; consumers spend their money on what is available. Government ownership of entire industries, as well as individual enterprises
centrally planned capitalism and economic system in which command resource allocation is utilized extensively in an environment of private resource ownership
market socialism -- Mark allocation policies are permitted within an overall environment of state ownership
G-7 -- Group of 7 -- high income countries, the United States, Japan, Germany, France, Britain, Canada, and Italy. Finance ministers, central bankers, and heads of state from the seven nations have worked together for a quarter of a century in an effort to steer the global economy in the direction of prosperity and to ensure monetary stability
Organization for Economic Cooperation and Development (OECD) -- institution comprised of high income countries, the 30 nations that belong to the OECD believe in market allocation economic systems and pluralistic democracy
The Triad -- Japan, Western Europe, and the United States. These three regions, represent the dominant economic centers of the world. Today, nearly 75% of the world income is located in the Triad
purchasing power parity (PPP) --Model of exchange rate determination stating that the price of a good in one country should equal the price of the same good in another country, exchanged at the current rate
economic exposure -- impact of currency fluctuations on the present by you of the companies expected future cash flows
transaction exposure -- arises when the companies activities result in sales or purchases denominated in foreign currencies
hedging --Reducing exposure to risk of loss resulting from fluctuations in exchange rates, commodity prices, interest rates etc
forward market -- a mechanism for buying and selling currencies and a preset price for future delivery
the global economic environment
Chapter 2 -- summary
The economic environment is a major determinant of global market potential and opportunity. In today's global economy, capital movements are the key driving force, production has become uncoupled from employment, and capitalism has vanquished communism. Based on patterns of resource allocation and ownership, the world's national economies can be categorized as market capitalism, centrally planned capitalism, centrally planned socialism, and market socialism. The final years of the 20th century were marked by a transition toward market capitalism in many countries that had been centrally controlled. However, there still exists a great disparity among the nations of the world in terms of economic freedom.
Countries can be categorized in terms of their stage of economic development: low income, lower -- middle income, upper -- middle income, and high income. Countries in the first two categories are sometimes known as less developed countries (LDCs). Upper middle income countries with high growth rates are often called newly industrializing economies (NIEs). Several of the world's economies are notable for their fast growth; the big emerging markets (BEMs) include China and India (low income), Poland, Turkey, and Indonesia (lower middle income), Argentina, Brazil, Mexico, and South Africa (upper middle income), and South Korea (high income). The group of seven (G7) and Organization for Economic Cooperation and Development (OECD) represent two initiatives by high income nations to promote democratic ideals and free-market policies throughout the rest of the world. Most of the world's income is located in the Triad, which is comprised of Japan, the United States, and Western Europe. Companies with global aspirations generally have operations in all three areas. Market potential for a product can be evaluated by determining product saturation levels in light of income levels.
A countries balance of payments is a record of its economic transactions with the rest of the world; this record shows whether a country has a trade surplus (value of exports exceeded by you of imports) or a trade deficit (by you of imports exceeds value of exports). Trade figures can be further divided into merchandise trade and services trade accounts; a country can run a surplus in both accounts, a deficit in both accounts, or a combination of the two. The US merchandise trade deficit was 549 billion in 2003. However, the US enjoys an annual service trade surplus. Overall, the United States is a debtor; Japan enjoys an overall trade surplus and serves as a creditor nation.
Foreign exchange provides a means for settling accounts in different currencies. The dynamics of international finance can have a significant impact on the nation's economy as well as the fortunes of individual companies. Currencies can be subject to evaluation as a result of actions taken by a countries central banker. Currency trading by international speculators can also lead to evaluation.
When a country's economy is strong or when demand for its goods is high, its currency tends to appreciate in value. When currency bodies fluctuate, firms face various types of economic exposure. These include transaction exposure and operating exposure. Firms can manage exchange-rate exposure by hedging, for example, by buying and selling currencies and the forward market.
The economic environment is a major determinant of global market potential and opportunity. In today's global economy, capital movements are the key driving force, production has become uncoupled from employment, and capitalism has vanquished communism. Based on patterns of resource allocation and ownership, the world's national economies can be categorized as market capitalism, centrally planned capitalism, centrally planned socialism, and market socialism. The final years of the 20th century were marked by a transition toward market capitalism in many countries that had been centrally controlled. However, there still exists a great disparity among the nations of the world in terms of economic freedom.
Countries can be categorized in terms of their stage of economic development: low income, lower -- middle income, upper -- middle income, and high income. Countries in the first two categories are sometimes known as less developed countries (LDCs). Upper middle income countries with high growth rates are often called newly industrializing economies (NIEs). Several of the world's economies are notable for their fast growth; the big emerging markets (BEMs) include China and India (low income), Poland, Turkey, and Indonesia (lower middle income), Argentina, Brazil, Mexico, and South Africa (upper middle income), and South Korea (high income). The group of seven (G7) and Organization for Economic Cooperation and Development (OECD) represent two initiatives by high income nations to promote democratic ideals and free-market policies throughout the rest of the world. Most of the world's income is located in the Triad, which is comprised of Japan, the United States, and Western Europe. Companies with global aspirations generally have operations in all three areas. Market potential for a product can be evaluated by determining product saturation levels in light of income levels.
A countries balance of payments is a record of its economic transactions with the rest of the world; this record shows whether a country has a trade surplus (value of exports exceeded by you of imports) or a trade deficit (by you of imports exceeds value of exports). Trade figures can be further divided into merchandise trade and services trade accounts; a country can run a surplus in both accounts, a deficit in both accounts, or a combination of the two. The US merchandise trade deficit was 549 billion in 2003. However, the US enjoys an annual service trade surplus. Overall, the United States is a debtor; Japan enjoys an overall trade surplus and serves as a creditor nation.
Foreign exchange provides a means for settling accounts in different currencies. The dynamics of international finance can have a significant impact on the nation's economy as well as the fortunes of individual companies. Currencies can be subject to evaluation as a result of actions taken by a countries central banker. Currency trading by international speculators can also lead to evaluation.
When a country's economy is strong or when demand for its goods is high, its currency tends to appreciate in value. When currency bodies fluctuate, firms face various types of economic exposure. These include transaction exposure and operating exposure. Firms can manage exchange-rate exposure by hedging, for example, by buying and selling currencies and the forward market.
introduction to global marketing
Chapter 1 -- vocabulary
Global marketing -- involves an understanding of specific concepts, considerations, and strategies that must be skillfully applied in conjunction with Universal marketing fundamentals to ensure success in global markets
value chain -- The set of activities required to design, procure, produce, market, distribute, and service a product or service
value equation -- value = benefits/price (money, time, effort, etc.)
competitive advantage -- The benefit for consumers and/or customers which competitors may find difficult or uneconomic to replicate
global industry -- competitive advantage can be achieved by integrating and leveraging operations on a worldwide scale
focus -- the concentration of attention on a core business or competence
global marketing strategy (GMS) --
global market participation -- the extent to which a company has operations in major world markets
ethnocentric orientation -- person/persons who assumes that his or her home country is superior to the rest of the world
polycentric orientation -- an attitude or outlook that describes management belief or assumption that each country in which he company does business is unique
regiocentric and geocentric orientations -- a re-geocentric focuses on a region and geocentric views the entire world as a potential market and strives to develop integrated world market strategies
Global marketing -- involves an understanding of specific concepts, considerations, and strategies that must be skillfully applied in conjunction with Universal marketing fundamentals to ensure success in global markets
value chain -- The set of activities required to design, procure, produce, market, distribute, and service a product or service
value equation -- value = benefits/price (money, time, effort, etc.)
competitive advantage -- The benefit for consumers and/or customers which competitors may find difficult or uneconomic to replicate
global industry -- competitive advantage can be achieved by integrating and leveraging operations on a worldwide scale
focus -- the concentration of attention on a core business or competence
global marketing strategy (GMS) --
global market participation -- the extent to which a company has operations in major world markets
ethnocentric orientation -- person/persons who assumes that his or her home country is superior to the rest of the world
polycentric orientation -- an attitude or outlook that describes management belief or assumption that each country in which he company does business is unique
regiocentric and geocentric orientations -- a re-geocentric focuses on a region and geocentric views the entire world as a potential market and strives to develop integrated world market strategies
introduction to global marketing
Chapter 1
A company that engages in global marketing focuses its resources on global marketing opportunities and threats. Successful global marketers such as Nestlé, Coca-Cola, and Honda use familiar marketing mix elements (the four P's) to create global marketing programs. Marketing, R&D, manufacturing, and other activities comprise a firm's value chain; firms can figure these activities to create superior customer value on a global basis. Global companies also maintain strategic focus while relentlessly pursuing competitive advantage. The marketing mix, value chain, competitive advantage, and focus are universal in their applicability, irrespective of whether a company does business only in the home country or has a presence in many markets around the world. However, in a global industry, companies that fail to pursue global opportunities risk being pushed aside by stronger global competitors.
A firm's global marketing strategy (GMS) can enhance its worldwide performance. The GMS addresses several issues. First is the nature of the marketing program in terms of the balance between a standardization (extension) approach to the marketing mix elements in the localization (adaptation) approach that is responsive to country or regional differences. Second is the concentration of marketing activities in a few countries or the dispersal of such activities across many countries. Third, the pursuit of global marketing opportunities requires cross-border coordination of marketing activities. Finally, a firm's GMS will address the issue of global market participation.
The importance of global marketing today can be seen in the company rankings compiled by the Wall Street Journal, Fortune, financial Times, and other publications. Whether ranked by revenues, market capitalization, or some other measure, most of the world's major corporations are active regionally or globally. The size of global markets for individual industries or product categories helps explain why companies "go global." Global markets for some product categories represent hundreds of billions of dollars in annual sales; other markets are much smaller. Whenever the size of the opportunity, successful industry competitors find that increasing revenues and profits means seeking markets outside the home country.
Company management to be classified in terms of its orientation toward the world: ethnocentric, polycentric, regiocentric, or geocentric. An ethnocentric orientation characterized as domestic and international companies;international companies pursue marketing opportunities outside the market by extending various elements of the marketing mix. A polycentric worldview predominates at a multinational company, where the marketing mix is adapted by country managers operating at autonomously. Managers at global and transnational companies are regio centric or geocentric in their orientation and pursue both extension and adaptation strategies in global markets.
Global marketings importance today is shaped by the dynamic interplay of several driving and restraining forces.
Driving forces include:
A company that engages in global marketing focuses its resources on global marketing opportunities and threats. Successful global marketers such as Nestlé, Coca-Cola, and Honda use familiar marketing mix elements (the four P's) to create global marketing programs. Marketing, R&D, manufacturing, and other activities comprise a firm's value chain; firms can figure these activities to create superior customer value on a global basis. Global companies also maintain strategic focus while relentlessly pursuing competitive advantage. The marketing mix, value chain, competitive advantage, and focus are universal in their applicability, irrespective of whether a company does business only in the home country or has a presence in many markets around the world. However, in a global industry, companies that fail to pursue global opportunities risk being pushed aside by stronger global competitors.
A firm's global marketing strategy (GMS) can enhance its worldwide performance. The GMS addresses several issues. First is the nature of the marketing program in terms of the balance between a standardization (extension) approach to the marketing mix elements in the localization (adaptation) approach that is responsive to country or regional differences. Second is the concentration of marketing activities in a few countries or the dispersal of such activities across many countries. Third, the pursuit of global marketing opportunities requires cross-border coordination of marketing activities. Finally, a firm's GMS will address the issue of global market participation.
The importance of global marketing today can be seen in the company rankings compiled by the Wall Street Journal, Fortune, financial Times, and other publications. Whether ranked by revenues, market capitalization, or some other measure, most of the world's major corporations are active regionally or globally. The size of global markets for individual industries or product categories helps explain why companies "go global." Global markets for some product categories represent hundreds of billions of dollars in annual sales; other markets are much smaller. Whenever the size of the opportunity, successful industry competitors find that increasing revenues and profits means seeking markets outside the home country.
Company management to be classified in terms of its orientation toward the world: ethnocentric, polycentric, regiocentric, or geocentric. An ethnocentric orientation characterized as domestic and international companies;international companies pursue marketing opportunities outside the market by extending various elements of the marketing mix. A polycentric worldview predominates at a multinational company, where the marketing mix is adapted by country managers operating at autonomously. Managers at global and transnational companies are regio centric or geocentric in their orientation and pursue both extension and adaptation strategies in global markets.
Global marketings importance today is shaped by the dynamic interplay of several driving and restraining forces.
Driving forces include:
- needs and wants
- technology
- transportation and communication improvements
- product costs
- quality
- world economic trends
- opportunity recognition to develop leverage by operating globaly
- market differences
- management myopia
- organizational culture
- national controls such as non-tariff barriers
Saturday, June 09, 2007
unit 4 summary
| Marketing Data Analysis |
| Marketing research is a systematic process used to identify and solve marketing-related problems and issues. Addressing the research questions or hypotheses, however, requires that the researcher engage in data analysis. We begin our focus on analysis by examining basic analytical procedures, variance and covariance analysis, correlation and regression, and discriminant analysis. Data Analysis Researchers typically conduct a preliminary analysis of the data before conducting in-depth data analysis. Such analysis helps to provide a basic understanding of and insight into the data. In fact, many marketing research projects do not go beyond basic data analysis. Basic analysis helps us understand data distribution and allows us to test for differences or associations between two means or two medians, but what happens if our research involves multiple variables of interest? The standard statistical tests for differences between more than two means are analyses of variance and covariance. Analysis of Variance and Covariance Analysis of variance (ANOVA) and analysis of covariance (ANCOVA) are used to examine the differences in the mean values of the dependent variable associated with the effect of the controlled independent variables. Essentially, ANOVA is used as a test of means for two or more populations. The null hypothesis, typically, is that all means all equal. For example, suppose a researcher was interested in examining whether heavy, medium, light, or non-users of cereals differed in their preference for Cereal A, measured on a nine-point scale. The null hypothesis that the four groups were not different in preference could be tested using ANOVA. If the set of independent variables, however, consisted of both categorical and metric variables, a researcher is likely to employ ANCOVA. For example, ANCOVA is useful if a researcher wanted to examine the preference of product use groups and loyalty groups, taking into account the respondents¡¦ attitudes towards nutrition and the importance they attached to breakfast as a meal. The last two variables can be measured on a Likert scale (metric), but both product use and brand loyalty represent categorical variables. Correlation and Regression Regression analysis is widely used to explain variation in market share, sales, brand preference, and other marketing results. In fact, we are often interested in summarizing the strength of association between two metric variables, as in the following situations: 1. How strongly are sales related to advertising expenditures? 2. Is there an association between market share and the size of the sales force? 3. Are consumers' perceptions of quality related to their perception of prices? The single most commonly used test of association between two metric variables is the Pearson product moment correlation, which demonstrates the strength of the linear relationship between the tested variables. Understanding the product moment correlation is critical in that it acts as the foundation for all correlation testing, including multiple regression techniques. Regression analyses are powerful and flexible procedures to analyze associative relationships between a metric dependent variable and one or more independent variables. Discriminant Analysis Finally, discriminant analysis is a technique for analyzing data for which the criterion or dependent variable is categorical, but the predictors or independent variables are interval in nature. In fact, examples of discriminant analysis abound in marketing research. This technique can be used to answer questions such as: 1. In terms of demographic characteristics, how do customers who exhibit store loyalty differ from those who do not? 2. Do the various market segments differ in their media consumption habits? 3. What are the distinguishing characteristics of consumers who respond to direct mail solicitations? |
discriminant analysis
Chapter 18
Discriminate analysis is useful for analyzing data when the criterion or dependent variable is categorical and a predictor or independent variables are interval scaled. When the criterion variable has two categories, the technique is known as two-group discriminate analysis. Multiple discriminate analysis refers to the case when three or more categories are involved.
Conducting discriminate analysis is a five step procedure:
In multiple discriminate analysis, if there are G groups and k predictors, it is possible to estimate up to the smaller of G - 1 or k discriminate functions. The first function has the highest ratio of between group to within group sums of squares. The second function, uncorrelated with the first, has the second highest ratio, and so on.
Discriminate analysis -- a technique for analyzing marketing research data when the criterion or dependent variable is categorical and the predictor or independent variables are interval in nature
discriminate functions -- the linear combination of independent variables developed by discriminate analysis that will best discriminate between the categories of the dependent variable
two-group discriminate analysis -- discriminate analysis technique where the criterion variable has two categories
multiple discriminate analysis -- discriminate analysis technique where the criterion variable involves three or more categories
discriminate analysis model -- the statistical model on which discriminate analysis is based
analysis sample -- part of the total sample that is used for estimation of the discriminate function
validation sample -- that part of the total sample used to check the results of the estimation sample
direct method -- an approach to discriminate analysis that involves estimating the discriminate function so that all the predictors are included simultaneously
stepwise discriminate analysis -- discriminate analysis in which the predictors are entered sequentially based on their ability to discriminate between the groups
characteristic profile -- an aide to interpreting discriminate analysis results by describing each group in terms of the group means for the predictor variables
hit ratio -- the percentage of cases correctly classified by the discriminate analysis
territorial map -- a tool for assessing discriminate analysis results that plots the group membership of each case on a graph
Mahalanobis procedure -- a stepwise procedure used in discriminate analysis to maximize a generalized measure of the distance between the two closest groups
Discriminate analysis is useful for analyzing data when the criterion or dependent variable is categorical and a predictor or independent variables are interval scaled. When the criterion variable has two categories, the technique is known as two-group discriminate analysis. Multiple discriminate analysis refers to the case when three or more categories are involved.
Conducting discriminate analysis is a five step procedure:
- first, formulating the discriminate problem requires identification of the objectives and the criterion and the predictor variables. The sample is divided into two parts. One part, the analysis sample, is used to estimate the discriminate function. The other part, the holdout sample, is reserved for validation.
- Estimation, the second step, involves developing a linear combination of the predictors, called discriminate functions, said that the groups differ as much as possible on the predictor values.
- Determination of statistical significance is the third step. It involves testing the null hypothesis that, in the population, the means of all discriminate functions in all groups are equal. If the null hypothesis is rejected, it is meaningful to interpret the results.
- The fourth step, the interpretation of discriminate weights or coefficients, it's similar to that in multiple regression analysis. Given the multicollinearity in the predictor variables, there is no unambiguous measure of the relative importance of the predictors and discriminating between the groups. However, some idea of the relative importance of the variables may be obtained by examining the absolute magnitude of the standardize discriminate function coefficients and by examining the structure correlations or discriminate loadings. These simple correlations between each predictor and the discriminate function represent the variance at the predictor shares with the function. Another aide to interpreting discriminate analysis results is to develop a characteristic profile for each group, based on the group means for the predictor variables.
- Validation, the fifth step, involves developing the classification matrix. The discriminate weights estimated by using the analysis sample are multiplied by the values of the predictor variables in the holdout sample to generate discriminate scores for the cases in the holdout sample. The cases are then assigned to groups based on their discriminate scores and an appropriate decision role. The percentage of cases correctly classified as determined and compared to the rate that would be expected by chance classification.
In multiple discriminate analysis, if there are G groups and k predictors, it is possible to estimate up to the smaller of G - 1 or k discriminate functions. The first function has the highest ratio of between group to within group sums of squares. The second function, uncorrelated with the first, has the second highest ratio, and so on.
Discriminate analysis -- a technique for analyzing marketing research data when the criterion or dependent variable is categorical and the predictor or independent variables are interval in nature
discriminate functions -- the linear combination of independent variables developed by discriminate analysis that will best discriminate between the categories of the dependent variable
two-group discriminate analysis -- discriminate analysis technique where the criterion variable has two categories
multiple discriminate analysis -- discriminate analysis technique where the criterion variable involves three or more categories
discriminate analysis model -- the statistical model on which discriminate analysis is based
analysis sample -- part of the total sample that is used for estimation of the discriminate function
validation sample -- that part of the total sample used to check the results of the estimation sample
direct method -- an approach to discriminate analysis that involves estimating the discriminate function so that all the predictors are included simultaneously
stepwise discriminate analysis -- discriminate analysis in which the predictors are entered sequentially based on their ability to discriminate between the groups
characteristic profile -- an aide to interpreting discriminate analysis results by describing each group in terms of the group means for the predictor variables
hit ratio -- the percentage of cases correctly classified by the discriminate analysis
territorial map -- a tool for assessing discriminate analysis results that plots the group membership of each case on a graph
Mahalanobis procedure -- a stepwise procedure used in discriminate analysis to maximize a generalized measure of the distance between the two closest groups
correlation and regression
Chapter 17
The product moment correlation coefficient, r , measures the linear association between two metric (interval or ratio scaled) variables. It's square,r2, measures the proportion of variation and one variable explained by the other. The partial correlation coefficient measures the association between two variables after controlling, or adjusting for, the affects of one or more additional variables. The order of the partial correlation indicates how many variables are being adjusted or controlled. Partial correlations can be very helpful for detecting spurious relationships.
Bivariate regression derives a mathematical equation between a single metric criterion variable and a single metric predictor variable. The equation is derived in the form of a straight line by using the least squares procedure. When the regression is run on standardized data, the intercept assumes a value of 0, and the regression coefficients are called beta weights. The strength of association is measured by the coefficient of determination, r2, which is obtained by computing a ratio of SSreg to SSy. The standard error of estimate is used to access the accuracy of prediction and may be interpreted as a kind of average error made in predicting Y from the regression equation.
Multiple regression involves a single dependent variable and to a more independent variables. The partial regression coefficient, b1 , represents the expected change in Y when X1 is changed by one unit and X2 through Xk are held constant. The strength of association is measured by the coefficient of multiple determination, R2. The significance of the overall regression equation may be tested by the overall F test. Individual partial regression coefficients may be tested for significance using the t test or the incremental F test. Scattergrams of the residuals, in which the residuals are plotted against the predicted values, time, or predictor variables, are useful for examining the appropriateness of the underlying assumptions and the regression model fitted.
In stepwise regression, the predictor variables are entered or renewed from the regression equation 1 at a time for the purpose of selecting a smaller subset of predictors that account for most of the variation in the criterion variable. Multicollinearity, or very high intercorrelations among the predictor variables, can result in several problems. Because the predictors are correlated, regression analysis provides no unambiguous measure of relative importance of the predictors. Cross validation examines whether the regression model continues to hold true for comparable data not used in estimation. It is a useful procedure for evaluating the regression model.
Nominal or categorical variables may be used as predictors by coding them as dummy variables. Multiple regression with dummy variables provide a general procedure for the analysis of variance and covariance.
Product moment correlation (r) -- a statistic summarizing the strength of association between two metric variables
covariance -- a systematic relationship between two variables in which a change in one implies a corresponding change in the other
partial correlation coefficient -- a measure of the association between two variables after controlling or adjusting for the effects of one or more additional variables
part correlation coefficient -- a measure of the correlation between Y and X when the linear affects of the other independent variables have been removed from X but not from Y
nonmetric correlation -- a correlation measure for two nonmetric variables that relies on rankings to compute the correlation
regression analysis -- a statistical procedure for analyzing associative relationships between a metric dependent variable and one or more independent variables
bivariate regression -- a procedure for deriving a mathematical relationship, in the form of an equation, between a single metric dependent variable in a single metric independent variable
least-squares procedure -- a technique for fitting a straight line to a scattergram by minimizing the square of the vertical distances of all the points from the line
multiple regression -- a statistical technique that simultaneously developed a mathematical relationship between two or more independent variables and on interval scale dependent variable
multiple regression model -- an equation used to explain the results of multiple regression analysis
residual -- the difference between the observed value of Yi and the value predicted by the regression equation ,Yi
stepwise regression -- a regression procedure in which the predictor variables enter or leave the regression equation when a time
multicollinearity -- a state of very high is intercorrelations among independent variables
Cross validation -- a test of validity that examines whether a model holds on comparable data not used in the original estimation
double cross validation -- a special form of validation in which the sample is split into halves. One half serves as the estimation sample in the other as a validation sample. The roles of the estimation and validation halves and then reversed, and the cross validation process repeated
The product moment correlation coefficient, r , measures the linear association between two metric (interval or ratio scaled) variables. It's square,r2, measures the proportion of variation and one variable explained by the other. The partial correlation coefficient measures the association between two variables after controlling, or adjusting for, the affects of one or more additional variables. The order of the partial correlation indicates how many variables are being adjusted or controlled. Partial correlations can be very helpful for detecting spurious relationships.
Bivariate regression derives a mathematical equation between a single metric criterion variable and a single metric predictor variable. The equation is derived in the form of a straight line by using the least squares procedure. When the regression is run on standardized data, the intercept assumes a value of 0, and the regression coefficients are called beta weights. The strength of association is measured by the coefficient of determination, r2, which is obtained by computing a ratio of SSreg to SSy. The standard error of estimate is used to access the accuracy of prediction and may be interpreted as a kind of average error made in predicting Y from the regression equation.
Multiple regression involves a single dependent variable and to a more independent variables. The partial regression coefficient, b1 , represents the expected change in Y when X1 is changed by one unit and X2 through Xk are held constant. The strength of association is measured by the coefficient of multiple determination, R2. The significance of the overall regression equation may be tested by the overall F test. Individual partial regression coefficients may be tested for significance using the t test or the incremental F test. Scattergrams of the residuals, in which the residuals are plotted against the predicted values, time, or predictor variables, are useful for examining the appropriateness of the underlying assumptions and the regression model fitted.
In stepwise regression, the predictor variables are entered or renewed from the regression equation 1 at a time for the purpose of selecting a smaller subset of predictors that account for most of the variation in the criterion variable. Multicollinearity, or very high intercorrelations among the predictor variables, can result in several problems. Because the predictors are correlated, regression analysis provides no unambiguous measure of relative importance of the predictors. Cross validation examines whether the regression model continues to hold true for comparable data not used in estimation. It is a useful procedure for evaluating the regression model.
Nominal or categorical variables may be used as predictors by coding them as dummy variables. Multiple regression with dummy variables provide a general procedure for the analysis of variance and covariance.
Product moment correlation (r) -- a statistic summarizing the strength of association between two metric variables
covariance -- a systematic relationship between two variables in which a change in one implies a corresponding change in the other
partial correlation coefficient -- a measure of the association between two variables after controlling or adjusting for the effects of one or more additional variables
part correlation coefficient -- a measure of the correlation between Y and X when the linear affects of the other independent variables have been removed from X but not from Y
nonmetric correlation -- a correlation measure for two nonmetric variables that relies on rankings to compute the correlation
regression analysis -- a statistical procedure for analyzing associative relationships between a metric dependent variable and one or more independent variables
bivariate regression -- a procedure for deriving a mathematical relationship, in the form of an equation, between a single metric dependent variable in a single metric independent variable
least-squares procedure -- a technique for fitting a straight line to a scattergram by minimizing the square of the vertical distances of all the points from the line
multiple regression -- a statistical technique that simultaneously developed a mathematical relationship between two or more independent variables and on interval scale dependent variable
multiple regression model -- an equation used to explain the results of multiple regression analysis
residual -- the difference between the observed value of Yi and the value predicted by the regression equation ,Yi
stepwise regression -- a regression procedure in which the predictor variables enter or leave the regression equation when a time
multicollinearity -- a state of very high is intercorrelations among independent variables
Cross validation -- a test of validity that examines whether a model holds on comparable data not used in the original estimation
double cross validation -- a special form of validation in which the sample is split into halves. One half serves as the estimation sample in the other as a validation sample. The roles of the estimation and validation halves and then reversed, and the cross validation process repeated
analysis of variance and covariance
Chapter 16
In ANOVA and ANCOVA, the dependent variable is metric in the independent variables are all categorical, or combinations of categorical and metric variables. One way ANOVA involves a single independent categorical variable. Interest lies in testing the null hypothesis that the category means are equal in the population. The total variation and the dependent variable is decomposed into two components: variation related to the independent variable and variation related to error. The variation is measured in terms of the sum of squares corrected for the mean (SS). The mean square is obtained by dividing the SS by the corresponding degrees of freedom (df). The null hypothesis of equal means is tested by an F statistic, which is the ratio of the mean square related to the independent variable to the mean square related to error.
N-way analysis of variance involves a simultaneous examination of two or more categorical independent variables. A major advantage is that the interactions between the independent variables can be examined. The significance of the overall effect, interaction terms, and main effects of individual factors are examined by appropriate F tests. It is meaningful to test the significance of main effects only of the corresponding interaction terms are not significant.
ANCOVA includes at least one categorical independent variable and at least one animal or metric independent variable. The metric independent variable, or covariate, is commonly used remove extraneous variation from the dependent variable.
When the analysis of variance is conducted on two or more factors, interactions can arise. And interaction occurs when the effective one independent variable on the dependent variable is different for different categories or levels of another independent variable. If the interaction is significant, it may be ordinal or disordinal. Disordinal an action may be of a non-crossover or crossover type. In balanced designs, the relative importance of factors in explaining the variation in the dependent variable is measured by omega squared. Multiple comparisons in the form of a priori or a posteriori contrasts can be used for examining differences among specific means.
And repeated measures analysis of variance, observations on each subject are obtained under each treatment condition. This design is useful for controlling the differences in subjects that exist prior to the experiment. Not metric analysis of variance involves examining the differences in the central tendencies of two or more groups when the dependent variable is measured on a ordinal scale. Multivariate analysis of variance (MANOVA) involves two or more metric dependent variables.
Analysis of variance (ANOVA) -- a statistical technique for examining the differences among means for two more populations
factors -- categorical independent variables. The independent variables must be all categorical (nonmetric) to use ANOVA
treatment -- in ANOVA, a particular combination of factor levels or categories
one-way analysis of variance -- an ANOVA technique in which there is only one factor
n-way analysis of variance -- an ANOVA model where two or more factors are involved
analysis of covariance (ANCOVA) -- an advanced analysis of variance procedure in which the effects of one or more metric scaled extraneous variables are renewed from the dependent variable before conducting the ANOVA
covariate -- and metric independent variable used in ANOVA
decomposition of the total variation -- in one-way ANOVA, separation of the variation observed in the dependent variable into the variation due to the independent variables plus the variation due to error
interaction -- when assessing the relationship between two variables, and interaction occurs if the effects of X1 depends on the level of X2, and vice versa
significance of the overall effect -- a test that some differences exist between some of the treatment groups
significance of interaction effect -- a test of the significance of the interaction between two or more independent variables
significance of the main effect -- a test of the significance of the main effect for each individual factor
ordinal interaction -- and interaction where the rank order of the effects attributable to one factor does not change across the levels of the second factor
disordinal interaction -- a change in the rank order of the effects of one factor across the levels of another
omega squared -- a measure indicating the proportion of the variation in the dependent variable explained by a particular independent variable or factor
contrasts -- in ANOVA, a method of examining differences among two or more means of the treatment groups
a priori contrasts -- contrasts that are determined before conducting the analysis, based on the researcher's theoretical framework
a postpriori contrasts -- contrast made after the analysis. These are generally multiple comparison tests
multiple comparison test -- a postpriori contrast that enable the researcher to construct generalized confidence intervals they can be used to make pairwise comparisons of all treatment means
repeated measures ANOVA -- an ANOVA technique used when respondents are exposed to more than one treatment condition and repeated measurements are obtained
nonmetric ANOVA -- an ANOVA technique for examining the difference in the central tendencies of more than two groups when the dependent variable is measured on an ordinal scale
k-sample median test -- non-parametric test that is used to examine differences among groups when the dependent variable is measured on an ordinal scale
Kruskal-Wallis one-way analysis of variance -- a nonmetric ANOVA test that uses the rank value of each case, not merely its location relative to the median
multivariate analysis of variance (MANOVA) -- an ANOVA technique using two or more metric dependent variables
In ANOVA and ANCOVA, the dependent variable is metric in the independent variables are all categorical, or combinations of categorical and metric variables. One way ANOVA involves a single independent categorical variable. Interest lies in testing the null hypothesis that the category means are equal in the population. The total variation and the dependent variable is decomposed into two components: variation related to the independent variable and variation related to error. The variation is measured in terms of the sum of squares corrected for the mean (SS). The mean square is obtained by dividing the SS by the corresponding degrees of freedom (df). The null hypothesis of equal means is tested by an F statistic, which is the ratio of the mean square related to the independent variable to the mean square related to error.
N-way analysis of variance involves a simultaneous examination of two or more categorical independent variables. A major advantage is that the interactions between the independent variables can be examined. The significance of the overall effect, interaction terms, and main effects of individual factors are examined by appropriate F tests. It is meaningful to test the significance of main effects only of the corresponding interaction terms are not significant.
ANCOVA includes at least one categorical independent variable and at least one animal or metric independent variable. The metric independent variable, or covariate, is commonly used remove extraneous variation from the dependent variable.
When the analysis of variance is conducted on two or more factors, interactions can arise. And interaction occurs when the effective one independent variable on the dependent variable is different for different categories or levels of another independent variable. If the interaction is significant, it may be ordinal or disordinal. Disordinal an action may be of a non-crossover or crossover type. In balanced designs, the relative importance of factors in explaining the variation in the dependent variable is measured by omega squared. Multiple comparisons in the form of a priori or a posteriori contrasts can be used for examining differences among specific means.
And repeated measures analysis of variance, observations on each subject are obtained under each treatment condition. This design is useful for controlling the differences in subjects that exist prior to the experiment. Not metric analysis of variance involves examining the differences in the central tendencies of two or more groups when the dependent variable is measured on a ordinal scale. Multivariate analysis of variance (MANOVA) involves two or more metric dependent variables.
Analysis of variance (ANOVA) -- a statistical technique for examining the differences among means for two more populations
factors -- categorical independent variables. The independent variables must be all categorical (nonmetric) to use ANOVA
treatment -- in ANOVA, a particular combination of factor levels or categories
one-way analysis of variance -- an ANOVA technique in which there is only one factor
n-way analysis of variance -- an ANOVA model where two or more factors are involved
analysis of covariance (ANCOVA) -- an advanced analysis of variance procedure in which the effects of one or more metric scaled extraneous variables are renewed from the dependent variable before conducting the ANOVA
covariate -- and metric independent variable used in ANOVA
decomposition of the total variation -- in one-way ANOVA, separation of the variation observed in the dependent variable into the variation due to the independent variables plus the variation due to error
interaction -- when assessing the relationship between two variables, and interaction occurs if the effects of X1 depends on the level of X2, and vice versa
significance of the overall effect -- a test that some differences exist between some of the treatment groups
significance of interaction effect -- a test of the significance of the interaction between two or more independent variables
significance of the main effect -- a test of the significance of the main effect for each individual factor
ordinal interaction -- and interaction where the rank order of the effects attributable to one factor does not change across the levels of the second factor
disordinal interaction -- a change in the rank order of the effects of one factor across the levels of another
omega squared -- a measure indicating the proportion of the variation in the dependent variable explained by a particular independent variable or factor
contrasts -- in ANOVA, a method of examining differences among two or more means of the treatment groups
a priori contrasts -- contrasts that are determined before conducting the analysis, based on the researcher's theoretical framework
a postpriori contrasts -- contrast made after the analysis. These are generally multiple comparison tests
multiple comparison test -- a postpriori contrast that enable the researcher to construct generalized confidence intervals they can be used to make pairwise comparisons of all treatment means
repeated measures ANOVA -- an ANOVA technique used when respondents are exposed to more than one treatment condition and repeated measurements are obtained
nonmetric ANOVA -- an ANOVA technique for examining the difference in the central tendencies of more than two groups when the dependent variable is measured on an ordinal scale
k-sample median test -- non-parametric test that is used to examine differences among groups when the dependent variable is measured on an ordinal scale
Kruskal-Wallis one-way analysis of variance -- a nonmetric ANOVA test that uses the rank value of each case, not merely its location relative to the median
multivariate analysis of variance (MANOVA) -- an ANOVA technique using two or more metric dependent variables
frequency distribution, cross tabulation, and hypothesis testing
Chapter 15
Basic data analysis provides viable insights and guides the rest of the data analysis as well as the interpretation of the results. A frequency distribution should be obtained for each variable in the data. This analysis produces a table of frequency counts, percentages, and cumulative percentages for all the values associated with that variable. It indicates the extent of out of range, missing, or extreme values. The mean, mode, and median of a frequency distribution are measures of central tendency. The variability of the distribution is described by the range, the variants or standard deviation, coefficient of variation, and interquartile range. Skewness and kurtosis provide an idea of the shape of the distribution.
Cross tabulations are tables that reflect the joint distribution of two or more variables. In cross tabulation, the percentages can be computed either column wise, based on column totals, or row wise, based on row totals. The general rule is to compete the percentages in the direction of the independent variable, across the dependent variable. Often the introduction of a third variable can't provide additional insights. The Chi Square statistic provides a test of the statistical significance of the observed association in a cross tabulation. The phi coefficient, contingency coefficient, Cramer's V, and the lambda coefficient provide measures of the strength of association between the variables.
Parametric and non-parametric tests are available for testing hypothesis related to differences. And the parametric case, the t test is used to examine hypotheses related to the population mean. Different forms of the t test are suitable for testing hypotheses based on one sample, two independent samples, or paired samples. In the nonparametric case, popular one sample tests include the Kolmogorov-Smirnov, chi-square, runs test, and the binomial test. For two independent nonparametric samples, the Mann-Whitney U test, median test and the Kolmogorov-Smirnov test can be used. For paired samples, the Wlicoxon matched-pairs signed-ranks test and assign tests are useful for examining hypotheses related to measures of location.
frequency distribution -- a mathematical distribution whose objective is to obtain a count of the number of responses associated with different values of one variable and to express these counts in percentage terms
measures of location -- a statistic that describes a location within a data set. Measures of central tendency described the center of the distribution
mean -- the average; that value obtained by summing all elements in a set and dividing by the number of elements
mode -- a measure of central tendency given as the value that occurs the most in a sample distribution
median -- a measure of central tendency given as the value above which half of the values fall and below which half of the values fall
measures of variability -- a statistic that indicates the distributions dispersion
range -- the difference between the largest and smallest values of distribution
interquartile range -- the range of distribution income passing the middle 50% of the observations
variants -- the mean squared deviation of all the values from the mean
standard deviation -- the square root of the variance
coefficient of variation -- a useful expression in sampling theory for the standard deviation as a percentage of the mean
skewness -- a characteristic of a distribution that assesses its symmetry about the mean
kurtosis -- a measure of the relative peakedness or flatness of the curve defined by the frequency distribution
null hypothesis -- a statement in which no difference or effect is expected. If the null hypothesis is not rejected, no changes will be made
alternative hypothesis -- a statement that some difference or effect is expected. Excepting the alternative hypothesis will lead to changes in opinions or actions
one tailed test -- a test of the null hypothesis where the alternative hypothesis is expressed directionally
two tailed test -- a test of the null hypothesis where the alternative hypothesis is not expressed directionally
test statistic -- a measure of how close the sample has come to the null hypothesis. It often follows a well-known distribution, such as the normal, t, or chi- squared distribution
type I error -- also known as Alpha error, occurs when a sample results lead to the rejection of a null hypothesis that is in fact true
level of significance -- the probability of making a type 1 error
type II error -- also known as beta error, occurs when the sample results lead to the non-rejection of a null hypothesis that is in fact false
power of a test -- the probability of rejecting the null hypothesis when it is in fact false and should be rejected
Cross tabulation -- a statistical technique that describes two or more variables simultaneously and results in tables that reflect the joint distribution of two or more variables that have a limited number of categories or distinct values
contingency table -- a cross tabulation table. It contains a cell for every combination of categories of the two variables
chi-square statistic -- the statistic used to test the statistical significance of the observed association and cross tabulation. It assists us in determining whether a systematic association exists between the two variables
chi-square distribution -- a skewed distribution and shape depends solely on the number of degrees of freedom. As the number of degrees of freedom increases, the chi-square distribution becomes more symmetrical
phi coefficient -- a measure of the strength of Association and the special case of a table with two rows and two columns
contingency coefficient (C) -- a measure of the strength of association in a table of any size
Cramer's V -- a measure of the strength of association used in tables larger than 2 x 2
asymmetric lambda -- a measure of the percentage improvement in predicting the value of the dependent variable, given the value of the independent variable and contingency table analysis. Lambda also varies between zero and one
symmetric lambda -- the symmetric lambda does not make an assumption about which variable is dependent. It measures the overall improvement when production is done in both directions
tau b -- test statistic that measures the association between two ordinal-level variables. It makes adjustment for ties and is most appropriate when the table of variables is square
tau c -- test statistic that measures the association between two ordinal-level variables. It makes adjustment for ties and is most appropriate when the table of variables is not square but a rectangle
Gamma -- test statistic that measures the association between two ordinal-level variables. It does not make an adjustment for ties
parametric tests -- hypothesis testing procedures that assume that the variables of interest are measured on at least an interval scale
non-parametric tests -- hypothesis testing procedures that assume that the variables are measured on a nominal or ordinal scale
t test -- a univariate hypothesis test using the t distribution, which is used in the standard deviation is unknown and the sample size is small
t statistic -- a statistic that assumes that the variable has a symmetric bell shaped distribution in the mean is known (or assumed to be known) and the population variants is estimated from the sample
t distribution -- symmetric bell shaped distribution that is useful for small sample testing
z test -- a univariate hypothesis test using the standard normal distribution
independent samples -- to samples that are not experimentally related. The measurement of one sample has no effect on the values of the second sample
f test -- a statistical test of the equality of the variances of two populations
f statistic -- the f statistic is computed as the ratio of two sample variances
f distribution -- a frequency distribution that depends on two sets of degrees of freedom -- the degrees of freedom in the numerator and the degrees of freedom in the denominator
paired samples -- and hypothesis testing, the observations are paired so that two sets of observations relate to the same respondents
paired samples t test -- a test for differences in the means of paired samples
Kolmogorov-Smirnov one-sample test - A one sample nonparametric goodness of fit test that compares the cumulative distribution function for a variable with a specified distribution
runs test -- a test of randomness for a dichotomous variable
binomial test -- a goodness of fit statistical test for dichotomous variables. It tests the goodness of fit of the observed number of observations in each category to the number expected under a specified binomial distribution
Mann-Whitney U test -- a statistical test for the variable measured on an ordinal scale comparing the difference in the location of two populations based on observations from two independent samples
two-sample median test -- non-parametric test statistic that determines whether two groups are drawn from populations with the same median. This test is not as powerful as the Mann- Whitney U
Kolmogorov-Smirnov two-sample test -- nonparametric test statistic that determines whether to his divisions are the same. It takes into account any differences in the two distributions including median, dispersion, and skewness
Wilcoxon matched-pairs signed-ranks test -- a nonparametric test that analyzes the differences between the paired observations, taking into account the magnitude of the differences
sign test -- a nonparametric test for examining differences in the location of two populations, based on paired observations, that compares only the signs of the differences between pairs of variables without taking into account the magnitude of the differences
Basic data analysis provides viable insights and guides the rest of the data analysis as well as the interpretation of the results. A frequency distribution should be obtained for each variable in the data. This analysis produces a table of frequency counts, percentages, and cumulative percentages for all the values associated with that variable. It indicates the extent of out of range, missing, or extreme values. The mean, mode, and median of a frequency distribution are measures of central tendency. The variability of the distribution is described by the range, the variants or standard deviation, coefficient of variation, and interquartile range. Skewness and kurtosis provide an idea of the shape of the distribution.
Cross tabulations are tables that reflect the joint distribution of two or more variables. In cross tabulation, the percentages can be computed either column wise, based on column totals, or row wise, based on row totals. The general rule is to compete the percentages in the direction of the independent variable, across the dependent variable. Often the introduction of a third variable can't provide additional insights. The Chi Square statistic provides a test of the statistical significance of the observed association in a cross tabulation. The phi coefficient, contingency coefficient, Cramer's V, and the lambda coefficient provide measures of the strength of association between the variables.
Parametric and non-parametric tests are available for testing hypothesis related to differences. And the parametric case, the t test is used to examine hypotheses related to the population mean. Different forms of the t test are suitable for testing hypotheses based on one sample, two independent samples, or paired samples. In the nonparametric case, popular one sample tests include the Kolmogorov-Smirnov, chi-square, runs test, and the binomial test. For two independent nonparametric samples, the Mann-Whitney U test, median test and the Kolmogorov-Smirnov test can be used. For paired samples, the Wlicoxon matched-pairs signed-ranks test and assign tests are useful for examining hypotheses related to measures of location.
frequency distribution -- a mathematical distribution whose objective is to obtain a count of the number of responses associated with different values of one variable and to express these counts in percentage terms
measures of location -- a statistic that describes a location within a data set. Measures of central tendency described the center of the distribution
mean -- the average; that value obtained by summing all elements in a set and dividing by the number of elements
mode -- a measure of central tendency given as the value that occurs the most in a sample distribution
median -- a measure of central tendency given as the value above which half of the values fall and below which half of the values fall
measures of variability -- a statistic that indicates the distributions dispersion
range -- the difference between the largest and smallest values of distribution
interquartile range -- the range of distribution income passing the middle 50% of the observations
variants -- the mean squared deviation of all the values from the mean
standard deviation -- the square root of the variance
coefficient of variation -- a useful expression in sampling theory for the standard deviation as a percentage of the mean
skewness -- a characteristic of a distribution that assesses its symmetry about the mean
kurtosis -- a measure of the relative peakedness or flatness of the curve defined by the frequency distribution
null hypothesis -- a statement in which no difference or effect is expected. If the null hypothesis is not rejected, no changes will be made
alternative hypothesis -- a statement that some difference or effect is expected. Excepting the alternative hypothesis will lead to changes in opinions or actions
one tailed test -- a test of the null hypothesis where the alternative hypothesis is expressed directionally
two tailed test -- a test of the null hypothesis where the alternative hypothesis is not expressed directionally
test statistic -- a measure of how close the sample has come to the null hypothesis. It often follows a well-known distribution, such as the normal, t, or chi- squared distribution
type I error -- also known as Alpha error, occurs when a sample results lead to the rejection of a null hypothesis that is in fact true
level of significance -- the probability of making a type 1 error
type II error -- also known as beta error, occurs when the sample results lead to the non-rejection of a null hypothesis that is in fact false
power of a test -- the probability of rejecting the null hypothesis when it is in fact false and should be rejected
Cross tabulation -- a statistical technique that describes two or more variables simultaneously and results in tables that reflect the joint distribution of two or more variables that have a limited number of categories or distinct values
contingency table -- a cross tabulation table. It contains a cell for every combination of categories of the two variables
chi-square statistic -- the statistic used to test the statistical significance of the observed association and cross tabulation. It assists us in determining whether a systematic association exists between the two variables
chi-square distribution -- a skewed distribution and shape depends solely on the number of degrees of freedom. As the number of degrees of freedom increases, the chi-square distribution becomes more symmetrical
phi coefficient -- a measure of the strength of Association and the special case of a table with two rows and two columns
contingency coefficient (C) -- a measure of the strength of association in a table of any size
Cramer's V -- a measure of the strength of association used in tables larger than 2 x 2
asymmetric lambda -- a measure of the percentage improvement in predicting the value of the dependent variable, given the value of the independent variable and contingency table analysis. Lambda also varies between zero and one
symmetric lambda -- the symmetric lambda does not make an assumption about which variable is dependent. It measures the overall improvement when production is done in both directions
tau b -- test statistic that measures the association between two ordinal-level variables. It makes adjustment for ties and is most appropriate when the table of variables is square
tau c -- test statistic that measures the association between two ordinal-level variables. It makes adjustment for ties and is most appropriate when the table of variables is not square but a rectangle
Gamma -- test statistic that measures the association between two ordinal-level variables. It does not make an adjustment for ties
parametric tests -- hypothesis testing procedures that assume that the variables of interest are measured on at least an interval scale
non-parametric tests -- hypothesis testing procedures that assume that the variables are measured on a nominal or ordinal scale
t test -- a univariate hypothesis test using the t distribution, which is used in the standard deviation is unknown and the sample size is small
t statistic -- a statistic that assumes that the variable has a symmetric bell shaped distribution in the mean is known (or assumed to be known) and the population variants is estimated from the sample
t distribution -- symmetric bell shaped distribution that is useful for small sample testing
z test -- a univariate hypothesis test using the standard normal distribution
independent samples -- to samples that are not experimentally related. The measurement of one sample has no effect on the values of the second sample
f test -- a statistical test of the equality of the variances of two populations
f statistic -- the f statistic is computed as the ratio of two sample variances
f distribution -- a frequency distribution that depends on two sets of degrees of freedom -- the degrees of freedom in the numerator and the degrees of freedom in the denominator
paired samples -- and hypothesis testing, the observations are paired so that two sets of observations relate to the same respondents
paired samples t test -- a test for differences in the means of paired samples
Kolmogorov-Smirnov one-sample test - A one sample nonparametric goodness of fit test that compares the cumulative distribution function for a variable with a specified distribution
runs test -- a test of randomness for a dichotomous variable
binomial test -- a goodness of fit statistical test for dichotomous variables. It tests the goodness of fit of the observed number of observations in each category to the number expected under a specified binomial distribution
Mann-Whitney U test -- a statistical test for the variable measured on an ordinal scale comparing the difference in the location of two populations based on observations from two independent samples
two-sample median test -- non-parametric test statistic that determines whether two groups are drawn from populations with the same median. This test is not as powerful as the Mann- Whitney U
Kolmogorov-Smirnov two-sample test -- nonparametric test statistic that determines whether to his divisions are the same. It takes into account any differences in the two distributions including median, dispersion, and skewness
Wilcoxon matched-pairs signed-ranks test -- a nonparametric test that analyzes the differences between the paired observations, taking into account the magnitude of the differences
sign test -- a nonparametric test for examining differences in the location of two populations, based on paired observations, that compares only the signs of the differences between pairs of variables without taking into account the magnitude of the differences
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